中心积和切尔马克-德尔加多晶格

Pub Date : 2024-07-04 DOI:10.1016/j.jpaa.2024.107769

William Cocke , Ryan McCulloch

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引用次数: 0

摘要

有限群的 Chermak-Delgado 网格是子群网格的一个模块化自偶子网格。我们证明了中心积的 Chermak-Delgado 网格包含相关中心因子的 Chermak-Delgado 网格的乘积。此外，我们还获得了 Chermak-Delgado 网格中元素的高度相对于它们在中心因子的 Chermak-Delgado 网格中的高度的信息。我们还探讨了如何将中心积用作研究 Chermak-Delgado 网格的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Central products and the Chermak–Delgado lattice

The Chermak–Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak–Delgado lattice of a central product contains the product of the Chermak–Delgado lattices of the relevant central factors. Furthermore, we obtain information about heights of elements in the Chermak–Delgado lattice relative to their heights in the Chermak–Delgado lattices of central factors. We also explore how the central product can be used as a tool in investigating Chermak–Delgado lattices.

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